Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#92482 | C2 | semidirect |
| 3. #14521205 | C2 | direct (N × H) |
| 4. C2×#11758423 | C2 | semidirect |
| 17. C2×#92482 | C22 | semidirect |
| 23. #11758423 | C22 | semidirect |
| 56. C23×C31 | Q16 | semidirect |
| 86. C22×C31 | C2×Q16 | semidirect |
| 102. C2×C31 | #451 | semidirect |
| 124. C31 | C2×#451 | semidirect |
| 156. C23 | #92482 | semidirect |
| 185. C22 | C2×#92482 | semidirect |
| 195. C2 | #14521205 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92482 | 2 |
| C2×#11758501 | 2 |
| #14521205 | 2 |
| C2×#11758423 | 2 |
| C2×C22⋊(C31⋊C8) | 2 |
| C23×Q8×C31 | 2 |
| C2×#451 | 31 |